Identification and selection rules of the spin-wave eigen-modes in a normally magnetized nano-pillar

TL;DR

This study investigates the spin-wave eigen-modes in a normally magnetized nano-pillar using Magnetic Resonance Force Microscopy, revealing how excitation methods and symmetry breaking influence mode spectra and their theoretical modeling.

Contribution

It provides a detailed analysis of how different excitation methods and symmetry-breaking affect spin-wave modes in nano-pillars, combining experimental and theoretical approaches.

Findings

Uniform RF field excites only $ ext{l}=0$ modes.

Circular RF Oersted field excites only $ ext{l}=+1$ modes.

Symmetry breaking mixes mode symmetries, enabling simultaneous excitation.

Abstract

We report on a spectroscopic study of the spin-wave eigen-modes inside an individual normally magnetized two layers circular nano-pillar (Permalloy$|$Copper$|$Permalloy) by means of a Magnetic Resonance Force Microscope (MRFM). We demonstrate that the observed spin-wave spectrum critically depends on the method of excitation. While the spatially uniform radio-frequency (RF) magnetic field excites only the axially symmetric modes having azimuthal index $\ell=0$, the RF current flowing through the nano-pillar, creating a circular RF Oersted field, excites only the modes having azimuthal index $\ell=+1$. Breaking the axial symmetry of the nano-pillar, either by tilting the bias magnetic field or by making the pillar shape elliptical, mixes different $\ell$-index symmetries, which can be excited simultaneously by the RF current. Experimental spectra are compared to theoretical prediction using both analytical and numerical calculations. An analysis of the influence of the static and dynamic dipolar coupling between the nano-pillar magnetic layers on the mode spectrum is performed.